/*=====================================================================*
 *                   Copyright (C) 2011 Paul Mineiro                   *
 * All rights reserved.                                                *
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 * Redistribution and use in source and binary forms, with             *
 * or without modification, are permitted provided that the            *
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 *     above copyright notice, this list of conditions and             *
 *     the following disclaimer.                                       *
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 *     * Redistributions in binary form must reproduce the             *
 *     above copyright notice, this list of conditions and             *
 *     the following disclaimer in the documentation and/or            *
 *     other materials provided with the distribution.                 *
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 *     * Neither the name of Paul Mineiro nor the names                *
 *     of other contributors may be used to endorse or promote         *
 *     products derived from this software without specific            *
 *     prior written permission.                                       *
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 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND              *
 * CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,         *
 * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES               *
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE             *
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 * Contact: Paul Mineiro <paul@mineiro.com>                            *
 *=====================================================================*/

#include "qfunc.h"
#include "polytomousrasch.c"

#include <string.h>

float
qfunc (float                            kappa,
       float                            logalpha,
       float*                           dlogalpha,
       float*                           ddlogalpha,
       unsigned int                     n_labels,
       const float*                     tau,
       const float*                     loglambda,
       const float*                     pz,
       const Rating*                    ratings,
       unsigned int                     n_ratings,
       const ParameterizedDistribution* priorlogalpha,
       float                            hq)
{
  float q = hq;

  *dlogalpha = 0;
  *ddlogalpha = 0;

  for (unsigned int i = 0; i < n_ratings; ++i)
    {
      float alphalambda = fastexp (logalpha + loglambda[ratings[i].worker]);

      for (unsigned int j = 0; j < n_labels; ++j)
        {
          float dbeta;
          float ddbeta;

#define taufunc(_k)                                             \
  ({                                                            \
     tau[ratings[i].worker * (n_labels - 1) + _k] + _k + 0.5;   \
  })
          q += pz[j] * 
               log_polytomous_rasch (ratings[i].rating,
                                     j,
                                     alphalambda,
                                     taufunc,
                                     n_labels - 1,
                                     dbeta,
                                     ddbeta);

          *dlogalpha += pz[j] * alphalambda * dbeta;
          *ddlogalpha += pz[j] * alphalambda * (dbeta + alphalambda * ddbeta);
        }
#undef taufunc
    }

  q += parameterized_distribution_logpdf (priorlogalpha,
                                          kappa,
                                          logalpha);

  *dlogalpha += parameterized_distribution_d1logpdf (priorlogalpha,
                                                     kappa,
                                                     logalpha);

  *ddlogalpha += parameterized_distribution_dd1logpdf (priorlogalpha,
                                                       kappa,
                                                       logalpha);

  return q;
}

void
dqfunc (float                            logalpha,
        unsigned int                     n_labels,
        const float*                     tau,
        float*                           dtau,
        const float*                     loglambda,
        float*                           dloglambda,
        const float*                     pz,
        const Rating*                    ratings,
        unsigned int                     n_ratings)
{
  for (unsigned int i = 0; i < n_ratings; ++i)
    {
      float alphalambda = fastexp (logalpha + loglambda[ratings[i].worker]);

      for (unsigned int j = 0; j < n_labels; ++j)
        {
          float dbeta;
          float ddbeta;
          float dtautmp[n_labels - 1];

#define taufunc(_k)                                             \
  ({                                                            \
     tau[ratings[i].worker * (n_labels - 1) + _k] + _k + 0.5;   \
  })
          log_polytomous_rasch_dtau (ratings[i].rating,
                                     j,
                                     alphalambda,
                                     taufunc,
                                     n_labels - 1,
                                     dbeta,
                                     ddbeta,
                                     dtautmp);

          dloglambda[ratings[i].worker] += pz[j] * alphalambda * dbeta;

          for (unsigned int k = 0; k + 1 < n_labels; ++k)
            {
              dtau[ratings[i].worker * (n_labels - 1) + k] +=
                pz[j] * dtautmp[k];
            }
        }
#undef taufunc
    }
}
